Information on Result #547759

There is no linear OA(3112, 204, F3, 69) (dual of [204, 92, 70]-code), because construction Y1 would yield
  1. OA(3111, 148, S3, 69), but
    • the linear programming bound shows that M ≥ 34269 689678 954827 771722 528323 125817 537099 985988 010230 663767 339699 553771 239936 / 338753 436767 266709 313125 > 3111 [i]
  2. OA(392, 204, S3, 56), but
    • discarding factors would yield OA(392, 150, S3, 56), but
      • the linear programming bound shows that M ≥ 380 530607 134695 199590 326105 296054 561976 304500 746203 230842 591578 312022 091639 435706 399387 387663 092379 / 4 623519 949937 639772 321756 933595 131069 999192 578955 859375 > 392 [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1No linear OOA(3112, 204, F3, 2, 69) (dual of [(204, 2), 296, 70]-NRT-code) [i]Depth Reduction
2No linear OOA(3112, 204, F3, 3, 69) (dual of [(204, 3), 500, 70]-NRT-code) [i]
3No linear OOA(3112, 204, F3, 4, 69) (dual of [(204, 4), 704, 70]-NRT-code) [i]
4No linear OOA(3112, 204, F3, 5, 69) (dual of [(204, 5), 908, 70]-NRT-code) [i]
5No digital (43, 112, 204)-net over F3 [i]Extracting Embedded Orthogonal Array